midterm1.s2

midterm1.s2 - 21A CALCULUS Monica. Vazirani Oct 22, 2007...

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Unformatted text preview: 21A CALCULUS Monica. Vazirani Oct 22, 2007 Midterm 1 Name: :QCslefi QD§ V2- ID: Section: 1. (30 points) Determine whether the following limits exist, and if so, evaluate them: ’_ W I / 2" u \ L a?“ ‘ ' /’>‘ ’l "2 +\ ‘ Q * --.7X+l a 11111 Wang—2H1 «- \xm w’k \Y A “i 1. \W t. ‘ :U—wo .l ** "x" ( INK . i ‘ 1 7.1: +51 21 xAQD 48> 7XA'SX 2X\ xfiqfip Y25( 7X3+<K_2x5 \m — * lg/"Il M + X"M rl"§/>\’ 1K1 7O 0 . 3m4—10x+4 ,. O‘O'N — - b. limwaom ‘ OV‘O .\ ” @rflflfi— -_ \m (is/22m .2“; sin LIE—71' \/ ‘ I . d. 11111$_.7r111(e( ELM”) : Sy‘vq {Q S\ ' [/3 Name: ID: Section: 2 2. (20 points) Consider the function g($) = :28. a. (10 pt) Find (show your work) and list ALL asyinptotes to the graph of y = 22:28, indicating whether they are vertical, horizontal, oblique. ) \v“v\ C239?) 1: ()0 \V“ of") Z / do he \r\0< m, axing. C,:3\&»\ KAU'Xfig \kf’) 0c XA ‘Cp \\"V\ ‘ (2Q : w \in (30K) 3 —- {>0 J‘VI(‘ 0J2) Ck, 3 (53, X ‘4 kc; X4 “94+ ) x >~ ‘ a’ 21:1 : 7k“)— \5 (\n <_;\/3\L\\\r( Q 5'“ M \ "\fi A—Q ‘ x4 fi'fimx * 8 3:5 Q 13 «if -...., _. “1* a % ’1fi ' “"‘“"""’w n. b. (10 pt) On the graph below, sketch the function, also drawing the asymptotes. xfi Name: ID: Section: 3 3. (12 points) Fill in the following SIX blanks in the following problem, which involves using the precise definition of limit. Verify that 12 walim I = 5, for 6 =1. (1) We are given 6 = 1. Set 6 = 4. [Which we know to do because we’ve already done our scratch work beforehand] Then we verify, whenever 0<lX‘9~L(|<6 (2) then 120 l7 — 5i < (3) .1, Suppose —4 < 17 — 24 < 4. Then 20 < < 28. Taking reciprocals and scaling 120 30 . 5 > > 7, so, subtracting 5 12 —’ O > —0 - 5 > —0. I 7 But since 1 > 0 and "T5 > —1 this implies l >1—20—5> ~I , (4) CD which exactly means that N ame: ID: Section: 4 4. (08 points) If (3 — $2) S S 3cosa: for all —§ < x < %, find limmho f(17). 'L \\N\ y£"x:% \«AQ .\ ’Eie'x; \ / N fir VC ‘ 5 g kg m BC,’\CL r4\ W M “‘s. XAO 5. (5 points) Determine the points at which the given function f = x/ 14 — 2:3 is continuous. Q‘K X\ V1) gym-4 \q \_) ova (1‘; AL ms 0y wu‘w “K .. 1x 7/ O \7 > x to . 05‘? (a QC] 7 1 6. (10 points) Show the equation 40 = c + 6 has a, solution c in the interval [0, 2]. \28‘ OGCX\:‘(X~X-Cc. Km \3 WANG.“ (WK 06m: ‘7’0/0-«(91 \"CD 3 —5 <0 (MIN:- ql—Dr Kc : 3% “> O ‘3 mg \VT 3mm is 8‘0"“ O<C<3~ “A” %(Q\;©' Name: ID: Section: 5 7. (15 points) Find the equation of the tangent line to y = Va; — 2 at w = 6. Show your work. La COP” wL A 96.6 m Aw. \‘m v, (6,, 0(6)}: {CU/LL) , / \Me &\uC\-€ 6% AW <2 \Hve is Q (6\ \W Q‘Cfi-‘Q \ -’ g r \ /“" 2 \m M" “‘0 \‘ \r’o \" .. r- _ v” w ~ 1 m +2 . M ~ M \x “‘ / \A-fio , \ 412i T. \m .1 ‘/L/ I; :16 MW“) w «s W + ;L ...
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This note was uploaded on 10/07/2008 for the course MATH 21A taught by Professor Osserman during the Spring '07 term at UC Davis.

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midterm1.s2 - 21A CALCULUS Monica. Vazirani Oct 22, 2007...

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